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A novel method to achieve the coherence control of spatiotemporal coherency vortices of spatially and temporally partially coherent pulsed vortex (STPCPV) beams is proposed. The influence of spatial and temporal coherence of the source on the phase distributions and the positions of spatiotemporal coherency vortices of the STPCPV beams propagating through fused silica is investigated in detail, for the first time to our knowledge. It is found that the coherence width and the coherence time of the incident beam can be regarded as a perfect tool for controlling the phase distribution and position of a spatiotemporal coherency vortex. The results obtained in this paper will benefit a number of applications relating to light-matter interaction, quantum entanglement, quantum imaging, optical trapping and spatiotemporal spin-orbit angular momentum coupling.

We develop a scaling law for a class of statistically nonstationary scalar optical fields, which ensures spectral invariance on their propagation into the far zone of a planar source. The invariance involves the constraint that the normalized far-zone spectrum must be the same in every direction of observation, as well as equal to the normalized area-averaged source spectrum. Thus, it additionally represents an extension of the earlier work by Wolf on stationary fields [Phys. Rev. Lett. 56, 1370 (1986)PRLTAO0031-900710.1103/PhysRevLett.56.1370] that assumed the normalized source spectrum as independent of position. We present examples of both nonstationary and stationary fields that satisfy the scaling law and extended spectral invariance. acceptedVersion

We study the laser arrays which are constructed by partially coherent beams with multi-Gaussian correlation function, i.e., circular, rectangular and elliptical multi-Gaussian Schell-model (MGSM) beam arrays. Analytical propagation formulas for circular, rectangular and elliptical MGSM beam arrays through a stigmatic ABCD optical system and in turbulent atmosphere are derived, with which the propagation properties of such laser arrays may be easily determined. It is found that in the near field, the irradiance distributions of circular, rectangular and elliptical MGSM beam arrays are mainly controlled by the distribution of beam arrays in the source plane. In the far field, the irradiance distributions of circular, rectangular and elliptical MGSM beam arrays in free space are determined by their correlation functions respectively; while in turbulent atmosphere, the correlation functions and turbulent atmosphere all influence the irradiance distributions, especially after enough long distance propagation, the turbulent atmosphere may change the irradiance distributions from non-circular symmetry to circular symmetry.

Generation of visible photons by upconverting materials under excitation by the near-infrared part of sunlight is very attractive for complete utilization of solar energy. Visible upconversion luminescence is efficiently generated in BaCl2:Ln3+ (Ho3+ or Pr3+) particles via excitation with broad band near-infrared part of sunlight. We observed greatly enhanced photocurrent response from the thin-film hydrogenated amorphous silicon solar cell covered with the upconversion layer of BaCl2:Ho3+ phosphor, which demonstrates a prospective application for near-infrared photoresponse devices.

Correlation singularities of partially coherent beams with multi-Gaussian correlation function (i.e., multi-Gaussian Schell-model beams) are studied. It is shown that there exist correlation singularities for scalar multi-Gaussian Schell-model (MGSM) beams, both in the source plane and in the output plane. We find the simple relation between the correlation singularities and the beam index M of MGSM beams, i.e., the number of ring dislocations equals M − 1 , which may be used to determine the beam index M .

The concept of cross-spectral purity of light, established by Mandel for stationary optical fields, is extended to nonstationary fields. Separability conditions that ensure the cross-spectral purity of nonstationary light are derived in the space-frequency and space-time domains. It is also shown that the property of cross-spectral purity is not strictly preserved on propagation of fields with any appreciable spectral bandwidth. Further, we introduce a method for generating cross-spectrally pure (stationary and nonstationary) fields from spatially incoherent light sources by means of achromatic Fourier-transform systems.

We report the fabrication of Eu-doped CaF2 films with an adjustable oxidation state of Eu ions such as Eu2+, Eu2+/Eu3+ or Eu3+ by the electro-deposition method, which are promising for luminescence converters for LEDs. Usually, the Eu2+ ion is unstable and can be very easily oxidized into the Eu3+ ion in solution. We reduced Eu3+ ions into Eu2+ ions by the electrochemical reduction method, and then incorporated Eu2+ ions into a CaF2 film during successive electro-deposition. We controlled the balance between Eu2+, Eu2+/Eu3+ and Eu3+ doped in the CaF2 thin film by regulating the parameters of the deposition solution (pH). More importantly, we controlled the luminescence from the Eu doped CaF2 film to generate pure blue luminescence, white luminescence, and red luminescence. These results not only provide a method for reducing Eu3+ ions into Eu2+ ions in solution, but also establish a new preparation technique for Eu2+/Eu3+ ion doped films and pave a new way for potential applications of Eu2+ doped luminescent materials.

We derived analytical expressions for the correlation of intensity fluctuations of a partially coherent Gaussian Schell-model plane-wave pulse scattered by deterministic and random media. Our results extend the study of correlation of intensity fluctuations at two space points for scattered stationary fields to that at two time points for scattered non-stationary fields.

We present mathematical models for temporally and spectrally partially coherent pulse trains with Laguerre-Gaussian and Hermite-Gaussian Schell-model statistics as extensions of the standard Gaussian Schell model for pulse trains. We derive propagation formulas of both classes of pulsed fields in linearly dispersive media and in temporal optical systems. It is found that, in general, both types of fields exhibit time-domain self-splitting upon propagation. The Laguerre-Gaussian model leads to multiply peaked pulses, while the Hermite-Gaussian model leads to doubly peaked pulses, in the temporal far field (in dispersive media) or at the Fourier plane of a temporal system. In both model fields the character of the self-splitting phenomenon depends both on the degree of temporal and spectral coherence and on the power spectrum of the field.

The scattering of a stochastic electromagnetic plane-wave pulse on a Gaussian-correlated, quasi-homogeneous random medium within the accuracy of the first-order Born approximation is investigated. Based on the mutual coherence matrix, the analytical formula for the average intensity, degree of temporal coherence and degree of polarization of the scattered field in the far zone is derived. The numerical calculations are performed in order to show the influence of the pulse duration, temporal coherence length, degree of polarization of the incident pulse and the properties of scatterer on the average intensity, degree of temporal coherence and degree of polarization of the scattered field. The validity of the results is also interpreted physically.

Two partially coherent pulsed sources with sinc Schell-model (SSM) correlations are introduced. The analytic formulas for the average intensities of random pulse ensembles generated by such pulse sources propagating in dispersive medium are derived, and used to investigate their evolution. It is illustrated that the first type of pulsed source can generate tunable far-field flat profiles controlled by temporal correlation parameter and dispersion coefficient. The average intensity of the pulse ensembles generated by the second type of sources can split from a single distribution into two symmetric parts.

We investigate a class of isodiffracting pulsed beams, which are superpositions of transverse modes supported by spherical-mirror laser resonators. By employing modal weights that, for stationary light, produce a Gaussian Schell-model beam, we extend this standard model to pulsed beams. We first construct the two-frequency cross-spectral density function that characterizes the spatial coherence in the space-frequency domain. By assuming a power-exponential spectral profile, we then employ the generalized Wiener-Khintchine theorem for nonstationary light to derive the two-time mutual coherence function that describes the space-time coherence of the ensuing beams. The isodiffracting nature of the laser resonator modes permits all (paraxial-domain) calculations at any propagation distance to be performed analytically. Significant spatiotemporal coupling is revealed in subcycle, single-cycle, and few-cycle domains, where the partial spatial coherence also leads to reduced temporal coherence even though full spectral coherence is assumed.

In a recent publication [Opt. Lett.42, 1512 (2017)OPLEDP0146-959210.1364/OL.42.001512], a novel class of partially coherent sources with circular coherence was introduced. In this paper, we examine the propagation behavior of the spectral density and the spectral degree of spatial coherence of a beam generated by such a source in free space and in oceanic turbulent media. It is found that the beam exhibits self-focusing, which is dependent on the initial coherence and the parameters of oceanic turbulence. The self-focusing phenomenon disappears when the initial coherence is high enough or the oceanic turbulence is strong. The area of high coherence appears in the center and along two diagonal lines. With increasing turbulence, the coherence area reduces gradually along one diagonal line and is retained along the other one. A physical interpretation of the self-focusing phenomenon is presented, and potential applications in optical underwater communication and beam shaping are considered.

Theoretical predictions of light beam interactions with jet engine exhaust are of importance for optimization of various optical systems, including LIDARs, imagers and communication links operating in the vicinity of aircrafts and marine vessels. Here we extend the analysis previously carried out for coherent laser beams propagating in jet engine exhaust, to the broad class of Gaussian Schell-Model (GSM) beams, being capable of treating any degree of coherence in addition to size and radius of curvature. The analytical formulas for the spectral density (SD) and the spectral degree of coherence (DOC) of the GSM beam are obtained and analyzed on passage through a typical jet engine exhaust region. It is shown that for sources with high coherence, the transverse profiles of the SD and the DOC of the GSM beams gradually transition from initially circular to elliptical shape upon propagation at very short ranges. However, such transition is suppressed for sources with lower coherence and disappears in the incoherent source limit, implying that the GSM source with low source coherence is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence. The physical interpretation and the illustration are included.

The statistical properties of stochastic electromagnetic beams passing through crystalline human eye onto the retina are studied. Using both the curved end faces and plane-parallel end faces models of human eye lens, a comparative study of the spectral density (SD), the spectral degree of polarization (SDOP) and the spectral degree of coherence (SDOC) of stochastic electromagnetic beams passing through crystalline human eye onto the retina is performed. It is shown that for the nearly incoherent electromagnetic beams, the SD and SDOP change non-monotonously with the propagation distance for plane-parallel end faces model, which is much different from the case when the human eye lens takes on curved end faces model, where the SD and SDOP change monotonously with the propagation distance. When the propagation distance is large enough, the SD decreases, whereas the SDOP and the SDOC increase with increasing lens thickness and decreasing lens equatorial radius, respectively. The validity of our results is interpreted physically.

A new class of partially coherent pulse sources with Multi-Gaussian Schell-model (MGSM) correlations is proposed. The expression for the intensity distribution for the MGSM pulses generated by such sources on propagation through the dispersive media is derived. It is demonstrated that the pulse intensity profile, in particular, the width of the flat center of pulse intensity profile and the peak intensity, can be controlled by adjusting the source temporal coherence. The obtained results have potential applications in pulse shaping for communication and media sensing or pulsed laser material processing.

We investigate the influence of incident pulse duration on the properties of femtosecond filamentation by numerical simulations. The filament intensity and plasma density are compared in the classical model and the full model under different incident pulse durations. Our results demonstrate the important role that higher-order Kerr effect (HOKE) plays in femtosecond laser filamentation, and the incident pulse duration has a significant influence on the relative contribution of HOKE, which consistently confirm the conclusions proposed by Loriot et al (2011 Laser Phys. 21 1319). Our findings provide a possible way to test the validity of the classical model and the full model in filamentation process by measuring the plasma density as a function of pulse duration through relevant experimental techniques.

With the help of the Rayleigh-Sommerfeld diffraction integral, an analytical formula for the spectral density of a nonparaxial polychromatic partially coherent (NPPC) standard or elegant Laguerre-Gaussian (LG) beam propagating through free space is derived. The evolution properties of the intensity distribution of a NPPC standard or elegant LG beam are studied numerically. It is found that the behavior of the intensity distribution of the NPPC standard or elegant LG beam is determined by the initial beam parameters (i.e., beam waist size, spatial coherence width and beam orders). Furthermore, we also study the influence of the initial beam parameters on the spectral change of a NPPC standard or elegant LG beam upon propagation in free space. It is shown that the on-axis spectral shift of a NPPC standard LG beam is almost the same with that of a NPPC elegant LG beam when the initial beam parameters of two type beams are identical. However, the difference between the off-axis spectral shift between a NPPC standard LG beam and a NPPC elegant LG beam is enhanced with the decrease of beam waist size or with the increase of spatial coherence width and beam mode orders.

The propagation behavior of the spectral degree of polarization of stochastic spatially and spectrally partially coherent electromagnetic flat-topped pulses in free space is studied. Numerical calculation results are given to illustrate the dependence of spectral degree of polarization on the beam order, pulse frequency, temporal coherence length, pulse duration and spatial correlation length. It is shown that with increasing beam order M the position z of the on-axis spectral degree of polarization P = 0 decreases, and the distribution of spectral degree of polarization is different for different values of M.

The scattering of a Multi-Gaussian Schell-model pulse from a sphere with semisoft boundaries within the accuracy of the first-order Born approximation is investigated. The analytic expression for the average intensity of the scattered pulse in the far zone is derived. The numerical calculations are performed in order to show the dependence of the average intensity of the scattered field on the incident pulse duration, the temporal coherence length of the incident pulse, the upper summation index and the effective radius of the medium. The effect of the boundary’s softness on the scattered intensity distribution is emphasized. It is shown that, comparing with that of scattering from a Gaussian sphere, the average intensity distribution of the pulse scattering from a sphere with semisoft boundaries has two or three peaks under certain circumstances.

The scattering of a partially coherent plane-wave pulse on a deterministic sphere is investigated. Analytical expression for the mutual coherence function of the scattered field is derived. It is shown that we can obtain the information of the sphereʼs position and its effective radius by measuring the time delay and pulse duration of the scattered field. The dependence of the pulse duration and temporal coherence length of the scattered field on the scattering angle and the parameters of the incident pulse is also illustrated numerically.

Based on the generalized Rayleigh–Sommerfeld diffraction integral, the analytical expression for 3×3 cross-spectral density matrix of nonparaxial spatially and spectrally partially coherent electromagnetic Cosh-Gaussian (ChG) pulsed beams propagating in free space is derived, and used to formulate the spectral density and spectral degree of polarization of electromagnetic pulsed beams at the z-plane. It is found that the parameters f and fαα are the key parameters in determining the nonparaxiality of spatially and spectrally partially coherent electromagnetic ChG pulsed beams. And the decentered parameter, pulse duration and temporal coherence length can change the nonparaxial behavior of the electromagnetic ChG pulsed beams. The effect of decentered parameter, pulse duration and temporal coherence length on the spectral density and spectral degree of polarization of electromagnetic ChG pulsed beams is illustrated through numerical calculations. Propagation of nonparaxial spatially and spectrally partially coherent electromagnetic Gaussian Schell-model pulsed beams can be treated as a special case when the decentered parameter of electromagnetic ChG pulsed beams approaches to zero.

The first-principles study on the mechanical stability, elastic and thermodynamic properties of WN 2 with P6 3 / mmc and P-6m2 phases are reported using the pseudopotential plane wave method within the generalized gradient approximation. The calculated equilibrium parameters are in good agreement with the available theoretical data. A complete elastic tensor and crystal anisotropies of the ultra-incompressible WN 2 are determined in the wide pressure range. By the elastic stability criteria, it is predicted that P6 3 / mmc and P-6m2 phases in WN 2 are not stable above 175.1 GPa and 170.1 GPa, respectively. Finally, by using the quasi-harmonic Debye model, the bulk modulus, relative volume, the coefficient of thermal expansion, and the Gruneisen parameter of WN 2 are also successfully obtained in the present work.

By using the generalized vectorial Rayleigh-Sommerfeld diffraction integral, the analytical expression for the spectral degree of polarization (SDP) of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams (SSSPCEPB) is derived, and used to study the changes in the SDP of SSSPCEPB in the nonparaxial regime. Similar to that of continuous beams, the f parameter and f αα parameter of pulsed beams also play an important role in determining the nonparaxiality of SSSPCEPB. However, the pulse duration and temporal coherence length of the pulse can change the nonparaxiality of SSSPCEPB. The dependence of SDP on the f parameter, pulse duration and temporal coherence length is emphasized and illustrated numerically.

The concept of the degree of cross-polarization is extended from stochastic electromagnetic stationary beams to stochastic electromagnetic pulsed beams, and the propagation properties of the degree of cross-polarization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams is studied. The influence of pulse duration and temporal coherence length on the degree of cross-polarization P is emphasized. It is shown that P exhibits an oscillatory behavior in free-space propagation. An increase in the pulse duration or a decrease in the temporal coherence length can weaken the oscillation of P . The validity of the results is interpreted physically.

The analytical expressions for the generalized (two-point) Stokes parameters of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams propagating in free space are obtained. The changes in the spectral Stokes parameters in free space propagation are studied. The dependence of on-axis and transverse spectral Stokes parameters of stochastic electromagnetic GSMP beams on the pulse parameters including pulse duration and temporal coherence length is stressed and illustrated numerically. The results are interpreted physically.

The analytical expression for the spectrum of spatially and spectrally partially coherent cosh-Gaussian pulsed (ChGP) beams focused by an aperture lens is derived and used to study their spectral properties at the focal plane and on the axis. The effect of the truncation parameter, spatial correlation parameter, decentered parameter and temporal coherence length on the spectral shifts and spectral switches of spatially and spectrally partially coherent ChGP beams is stressed. The results are illustrated numerically and interpreted physically.

By using the generalized Huygens–Fresnel diffraction integral, the analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse of apertured stochastic electromagnetic modified Bessel–Gauss beams (MBGBs) through a paraxial optical ABCD system are derived, and used to study the changes in the state of polarization of apertured stochastic electromagnetic MBGBs propagating in free space. The invariance of the on-axis state of polarization of unapertured stochastic electromagnetic MBGBs propagating through paraxial optical ABCD systems is illustrated analytically and numerically. For apertured stochastic electromagnetic MBGBs, the on-axis spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse increase with increasing propagation distance, and approach asymptotic values when the propagation distance is large enough. There is a uniform distribution region of the state of polarization around the center of the beams whose range decreases with increasing truncation parameter. In addition, the state of polarization of apertured stochastic electromagnetic MBGBs upon propagation can be modulated by controlling the truncation parameter.

The spectral and spatiotemporal properties of Bessel–Gauss pulsed beams focused by a dispersive aperture lens are studied, where the dispersion of the first, second, and higher orders is taken into consideration. It is shown that the spectral switches take place at the geometrical focal plane, and the dispersion of the first order leads to a shift of the critical position towards the z-axis. The dispersion plays a noticeable role in the spatiotemporal intensity distribution. The dispersion of the first order results in a decrease of the peak intensity, in a shift and a broadening of the pulse form, and the effect becomes more noticeable with increasing waist width. The dispersion of the second order results in a further broadening and a decrease of the peak intensity, and the effect is larger as the thickness of the lens increases. However, the dispersion of the higher order plays a relatively minor role. The results are illustrated by numerical examples and interpreted physically.

The analytical expressions for the spectral degree of coherence and spectral intensity of spatially and spectrally partially coherent cosh-Gaussian pulsed (ChGP) beams propagating in free space are derived. It is shown that the spectral degree of coherence and spectral intensity of spatially and spectrally partially coherent ChGP beams depend on the spatial correlation parameter, decentered parameter and temporal coherence length. Depending on the decentered parameter, the effective width of the spectral degree of coherence can be larger than, smaller than or equal to that of the spectral intensity. The results are illustrated by numerical examples.

The phase singularities and spectral switches of focused higher-order Bessel–Gauss pulsed beams are studied. Numerical calculation results are given to illustrate the dependence of phase singularities and spectral switches of focused higher-order Bessel–Gauss pulsed beams on the truncation parameter, topological charge, spatial parameter and propagation distance. It is shown that there always exists an optical vortex at the center of focused higher-order Bessel–Gauss pulsed beams and the topological charge is conserved during the propagation. The spectral switch appears in the neighborhood of the zero- or minimum-intensity position. With increasing topological charge or spatial parameter, the size of the vortex core increases and the spectral transition height decreases.

Taking the Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the far-field spectrum of diffracted GSMP beams in Young’s interference experiment is derived, and used to study the spectral shifts and spectral switches of GSMP beams in the far field. Numerical calculation results are given to illustrate the dependence of spectral shifts and spectral switches on the obscuration ratio e , temporal coherent length T c , spatial correlation parameter β and diffraction angle α . It is shown that the critical angle α c of the first- and second-order spectral switches moves away from the z axis with increasing T c , but α c of the third-order spectral switch moves towards the z axis with increasing T c . The spectral transition height Δ decreases and spectral minimum S min increases as T c increases. α c decreases, Δ increases and S min decreases as β increases. The potential application of spectral switches of spatially and spectrally partially coherent pulsed beams in information encoding and transmission is proposed.

Starting from the propagation law of partially coherent light, the on-axis spectral shifts and spectral switches of Gaussian Schell-model (GSM) beams focused by an astigmatic aperture lens are studied. It is shown that, as compared with an aberration-free case whose spectral shifts and spectral switches are induced by spatial correlation and aperture diffraction, the spectral shifts and spectral switches of GSM beams also depend upon the astigmatism of the lens for an astigmatism case. Detailed numerical calculations are made to illustrate the behavior of spectral shifts and spectral switches of GSM beams focused by an astigmatic aperture lens.

Starting from the Huygens–Fresnel diffraction integral, the analytical expression for the power spectrum of pulsed Bessel beams focused by a dispersive aperture lens is derived and used to study the spectral anomalies of pulsed Bessel beams in the focused field. Numerical calculation results are given to illustrate the dependence of spectral anomalous behavior on the pulse parameters, truncation parameter and material dispersion of the lens. It is shown that near the phase singularities the spectral anomalies may take place. The potential applications of spectral anomalies of ultrashort pulsed beams in information encoding and information transmission are considered.

Starting from the propagation law of partially coherent light, the focusing properties of twisted Gaussian Schell-model (TGSM) beams passing through an optical system consisting of an aperture lens or through a system consisting of a separated aperture and lens are studied. The propagation expressions for focused TGSM beams have been derived. Our main attention is focused on the effect of the coherence of partially coherent light, the twist parameter and the distance between the aperture and lens on the focusing properties of TGSM beams. Numerical calculation results are given to illustrate how the coherence of partially coherent light, the twist parameter and the distance between the aperture and lens affect the axial irradiance in the focused field.

Starting from the Huygens–Fresnel diffraction integral, the recurrence expressions for the power spectra of pulsed Hermite–Gaussian (H–G) beams focused by a dispersive aperture lens are derived and the spectral anomalies of pulsed H–G beams in the focused field are studied. Numerical results are given to illustrate the dependence of spectral anomalies’ behavior on the pulse parameters, truncation parameter and material dispersion of the lens. The potential applications of spectral anomalies of ultrashort pulsed beams in information encoding and information transmission are considered.

Starting from the Huygens–Fresnel diffraction integral, the recurrence expression for the power spectra of pulsed Hermite–Gaussian beams in Young’s interference experiment in dispersive media are derived and used to study the spectral anomalies of pulsed Hermite–Gaussian beams in the far field. The results of numerical calculation are given to illustrate the dependence of spectral anomalous behavior on the pulse parameter, slit parameter, diffraction angle and dispersive property of medium. The potential application of spectral anomalies of pulsed Hermite–Gaussian beams in information encoding and information transmission in dispersive media is considered.

Based on the beam coherent-polarization (BCP) matrix approach and propagation law of partially coherent beams, the focal shift and focal switch of partially polarized Gaussian Schell-model (PGSM) beams passing through a system with the aperture and spherically aberrated lens separated is studied in detail. Our main attention is focused on the effect of spherical aberration and partial coherence on the focal shift and focal switch of PGSM beams. It is shown that for polarizer-free case there is no focal switch of PGSM beams, the focal shift of PGSM beams is closely related with spherical aberration coefficient C4, auto-coherence length σa, truncation parameter δ and relative position s/f between the aperture and lens in general, and is independent of the cross-coherence length σc. After inserting a polarizer the focal switch can take place. Numerical calculation results are given to illustrate how the spherical aberration and partial coherence affect the focal shift and focal switch of PGSM beams.

Starting from the propagation law of partially coherent light, the spectrum of twisted Gaussian Schell-model (TGSM) beams passing through an aperture is studied. Detailed numerical calculation results are presented, and illustrated. It is shown that the spectral shifts and switches can also take place for TGSM beams, and as compared with the aberration-free Gaussian Schell-model (GSM) beams case, the twist factor affects the spectral shifts and spectral switches. Numerical calculation results are given to illustrate how the twist factor affects the spectral behavior.